If f(x) = x – [x], where [x] represents the greatest integer less than or equal to x, then the range of f(x) is given by
Explanation:
The function f(x) represents the fractional part of the function as it is the difference between x and the greatest integer function. For example, if x = 0.499 ⇒ f(x) = 0.499 – 0 = 0.499 If x = 1 ⇒ f(x) = 1 – 1 = 0 ∴ The value of this function will always lie between 0 and 1 for all positive and negative values of x. The range will include 0 as this will be the value when x is an integer but will never include 1. ∴ Range of f(x) = [0, 1) Hence, option (c).
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